Solve (3ab)^-3*4a^2b^4

$$( 3 a b ) ^ { - 3 } \times 4 a ^ { 2 } b ^ { 4 }$$

Evaluate

$$\frac{4b}{27a}$$

Solution Steps

Expand \left(3ab\right)^{-3}.

$$3^{-3}a^{-3}b^{-3}\times 4a^{2}b^{4}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{27}a^{-3}b^{-3}\times 4a^{2}b^{4}$$

Multiply \frac{1}{27} and 4 to get \frac{4}{27}.

$$\frac{4}{27}a^{-3}b^{-3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add -3 and 2 to get -1.

$$\frac{4}{27}a^{-1}b^{-3}b^{4}$$

To multiply powers of the same base, add their exponents. Add -3 and 4 to get 1.

$$\frac{4}{27}a^{-1}b^{1}$$

Calculate b to the power of 1 and get b.

$$\frac{4}{27}a^{-1}b$$

Expand

$$\frac{4b}{27a}$$

Solution Steps

Expand \left(3ab\right)^{-3}.

$$3^{-3}a^{-3}b^{-3}\times 4a^{2}b^{4}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{27}a^{-3}b^{-3}\times 4a^{2}b^{4}$$

Multiply \frac{1}{27} and 4 to get \frac{4}{27}.

$$\frac{4}{27}a^{-3}b^{-3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add -3 and 2 to get -1.

$$\frac{4}{27}a^{-1}b^{-3}b^{4}$$

To multiply powers of the same base, add their exponents. Add -3 and 4 to get 1.

$$\frac{4}{27}a^{-1}b^{1}$$

Calculate b to the power of 1 and get b.

$$\frac{4}{27}a^{-1}b$$